A Scalable Byzantine Grid

Modern networks assemble an ever growing number of nodes. However, it remains difficult to increase the number of channels per node, thus the maximal degree of the network may be bounded. This is typically the case in grid topology networks, where each node has at most four neighbors. In this paper, we address the following issue: if each node is likely to fail in an unpredictable manner, how can we preserve some global reliability guarantees when the number of nodes keeps increasing unboundedly ? To be more specific, we consider the problem or reliably broadcasting information on an asynchronous grid in the presence of Byzantine failures -- that is, some nodes may have an arbitrary and potentially malicious behavior. Our requirement is that a constant fraction of correct nodes remain able to achieve reliable communication. Existing solutions can only tolerate a fixed number of Byzantine failures if they adopt a worst-case placement scheme. Besides, if we assume a constant Byzantine ratio (each node has the same probability to be Byzantine), the probability to have a fatal placement approaches 1 when the number of nodes increases, and reliability guarantees collapse. In this paper, we propose the first broadcast protocol that overcomes these difficulties. First, the number of Byzantine failures that can be tolerated (if they adopt the worst-case placement) now increases with the number of nodes. Second, we are able to tolerate a constant Byzantine ratio, however large the grid may be. In other words, the grid becomes scalable. This result has important security applications in ultra-large networks, where each node has a given probability to misbehave.Comment: 17 page

Reliability of Partial k-tree Networks

133 pagesRecent developments in graph theory have shown the importance of the class of partial k- trees. This large class of graphs admits several algorithm design methodologies that render efficient solutions for a large number of problems inherently difficult for general graphs. In this thesis we develop such algorithms to solve a variety of reliability problems on partial k-tree networks with node and edge failures. We also investigate the problem of designing uniformly optimal 2-trees with respect to the 2-terminal reliability measure. We model a. communication network as a graph in which nodes represent communication sites and edges represent bidirectional communication lines. Each component (node or edge) has an associated probability of operation. Components of the network are in either operational or failed state and their failures are statistically independent. Under this model, the reliability of a network G is defined as the probability that a given connectivity condition holds. The l-terminal reliability of G, Rel1 ( G), is the probability that any two of a given set of I nodes of G can communicate. Robustness of a network to withstand failures can be expressed through network resilience, Res( G), which is the expected number of distinct pairs of nodes that can communicate. Computing these and other similarly defined measures is #P-hard for general networks. We use a dynamic programming paradigm to design linear time algorithms that compute Rel1( G), Res( G), and some other reliability and resilience measures of a partial k-tree network given with an embedding in a k-tree (for a fixed k). Reliability problems on directed networks are also inherently difficult. We present efficient algorithms for directed versions of typical reliability and resilience problems restricted to partial k-tree networks without node failures. Then we reduce to those reliability problems allowing both node and edge failures. Finally, we study 2-terminal reliability aspects of 2-trees. We characterize uniformly optimal 2-trees, 2-paths, and 2-caterpillars with respect to Rel2 and identify local graph operations that improve the 2-terminal reliability of 2-tree networks

Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.Comment: 7 pages, 4 figure

Fault-tolerant relay deployment for k node-disjoint paths in wireless sensor networks

Ensuring that wireless sensor networks (WSNs) are robust to failures requires that the physical network topology will offer alternative routes to the sinks. This requires sensor network deployments to be planned with an objective of ensuring some measure of robustness in the topology, so that when failures occur that routing protocols can continue to offer reliable delivery. Our contribution is a solution that enables fault-tolerant WSN deployment planning by judicious use of a minimum number of additional relay nodes. A WSN is robust if at least one route to a sink is available for each remaining sensor node after the failure of up to k-1 nodes. In this paper, we define the problem for increasing WSN reliability by deploying a number of additional relay nodes to ensure that each sensor node in the initial design has k node-disjoint paths to the sinks. We present GRASP-ARP, a centralised offline algorithm to be run during the initial topology design to solve this problem. We have implemented this algorithm and demonstrated in simulation that it improves the efficiency of relay node placement for k node-disjoint paths compared to the most closely related published algorithms

Resilience Model for Teams of Autonomous Unmanned Aerial Vehicles (UAV) Executing Surveillance Missions

Teams of low-cost Unmanned Aerial Vehicles (UAVs) have gained acceptance as an alternative for cooperatively searching and surveilling terrains. These UAVs are assembled with low-reliability components, so unit failures are possible. Losing UAVs to failures decreases the team\u27s coverage efficiency and impacts communication, given that UAVs are also communication nodes. Such is the case of a Flying Ad Hoc Network (FANET), where the failure of a communication node may isolate segments of the network covering several nodes. The main goal of this study is to develop a resilience model that would allow us to analyze the effects of individual UAV failures on the team\u27s performance to improve the team\u27s resilience. The proposed solution models and simulates the UAV team using Agent-Based Modeling and Simulation. UAVs are modeled as autonomous agents, and the searched terrain as a two-dimensional M x N grid. Communication between agents permits having the exact data on the transit and occupation of all cells in real time. Such communication allows the UAV agents to estimate the best alternatives to move within the grid and know the exact number of all agents\u27 visits to the cells. Each UAV is simulated as a hobbyist, fixed-wing airplane equipped with a generic set of actuators and a generic controller. Individual UAV failures are simulated following reliability Fault Trees. Each affected UAV is disabled and eliminated from the pool of active units. After each unit failure, the system generates a new topology. It produces a set of minimum-distance trees for each node (UAV) in the grid. The new trees will thus depict the rearrangement links as required after a node failure or if changes occur in the topology due to node movement. The model should generate parameters such as the number and location of compromised nodes, performance before and after the failure, and the estimated time of restitution needed to model the team\u27s resilience. The study addresses three research goals: identifying appropriate tools for modeling UAV scenarios, developing a model for assessing UAVs team resilience that overcomes previous studies\u27 limitations, and testing the model through multiple simulations. The study fills a gap in the literature as previous studies focus on system communication disruptions (i.e., node failures) without considering UAV unit reliability. This consideration becomes critical as using small, low-cost units prone to failure becomes widespread